Cavitation retarding blade and a method of delaying the occurrence of cavitation to increased blade velocities



May 26, 1942 l L. P. SMITH 2,283,956 CAVITATION RE RDING BLADE AND AMETHOD OF DELAYING OCCURRENCE OF CAVITATION TO INC REASED BLADE VELOCITIFiled June 21, l937 TRAIL/N6 5045 FIG 2 I INVENTOR LYBRAND I? SMITHATTORNEY Patented May 26, 1942 UNITED STATE S PATENT OFFICE CAVITATIONRETARDING BLADE AND A METHOD OF DELAYING THE OCCURRENCE OF CAVITATION TOINCREASED BLADE VELOCITIES Lybrand P. Smith, United States NavyApplication June 21, 1937, Serial No. 149,543

' 6 Claims. (01. 170-159) (Granted under the act of March a, 1883, is

amended April 30, 1928;370 0. 0.157) 1 the pressure in the free streamand hence suction is present. The-suction side of the blade with whichthe present invention is concerned is the back of the bladeythe face ofthe blade bein the pressure side. Thus, when considering a marinepropeller the face denotes the driving face or that which pushes thewater astern when the propeller is in motion, while the work backnaturally denotes the surface opposite the face.

Whenever pressure on the back or suction side is reduced to vaporpressure, the water in that location boils and the blade will be inburbling cavitation.

Although back cavitation cannot be eliminated its development can,nevertheless, be delayed or deferred and this I accomplish in a new andnovel manner based on my researches on this subject. The usual pressuredistribution on the suction or backside of the blade shows-a suctionincreasing from the leading edge to a more or less vision of a. new andnovel back configuration which will insure the maintenance oftheaforesaid pressure distribution. The present invention is restrictedsolely to blades adapted for movement in a liquid fluid 'medium and isnotconcerned with aerial propellers. For what is sometimes calledburbling" in aerodynamics is a phenomenon totally different from theburbling cavitation encountered in connection with marine propeller andwater turbine blades.

Marine propellers are usually designed with reference to developedsections of the blade taken along a flow line, a flow line being thepath traced across the blade by any droplet of water which'just grazesthe leading edge and remains in contact with the blade until it leavesthe trailing edge. If, therefore, a cross section of the blade is takenat the flow line and developed on a plane, a developed section will beformed. In'the specification and claims hereinafter, the term developedblade section will be used in the sense here described.

As illustrating the formation of a developed section in the case ofconventional marine proprominent peak and gradually declining towards 4the trailing edge. Obviously before the blade can suction will havereached vaporpressure and burbling cavitation willexist. If, however,the suction were distributed substantially uniformly over the back 'ofthe blade, thus avoiding any appreciable peak,'the same total lift couldbe exerted .without the suction reaching vapor pressure. Thus, underthese conditions the blade would resist and delaythe occurrence ofburbling cavitation. Eventually, as the'speed of the blade is augmentedits suction will increase until vapor pressure is reached. This,however, will occur practically simultaneously over the whole blade withthe result that burbling cavitation will'take place over theentire bladeback or suction side from leading to trailing edge. a

My invention thus contemplates a method of delaying the occurrence ofburbling cavitation on the back of marine propellegoreavater iurbineblades by maintaining a-substantially uniform pressure distributionthereover as well as the probe producing its maximum lift the peak ofthe peller and propeller type turbine blades, it is noted that the flowline of these-blades lies approximately on the surface of a cylinder,the axis of which conincides with the propeller 'or turbine shaft. If,therefore, a section of either blade is cut at the desired'radius by theconcentric cylinder and developed on a plane, a developed blade sectionwill be formed.

I have discovered that my new and novel blade, if it is to maintain asubstantially uniform pressure distribution on the back thereof andthereby delay the occurrence of burbling cavitation, must have abackwhich in any developed section of the blade is substantially ellipticalin shape or closely approximates that of an ellipse.

The method of arriving at this developed blade section will be pointedout in detail hereinafter.

In the light of the foregoing, it is clear that it is an object of myinvention to provide a blade adapted for movement in a liquid fluidmedium the back of which is of such a configuration as to delay theoccurrence of burbling cavitation;

and that it is another object of my invention to provide a method ofdelaying the occurrence of burbling cavitation occasioned by themovement Avantages of this invention will be readily appreciated as thesame becomes better understood by reference to the following detaileddescription panying sheet of drawings wherein:

Fig. 1 shows superimposed on one another for comparison purposesdeveloped sections of a blade with a standard, prior art. ogival orcircular arc back; the new elliptical back; a new quasi-elliptical backapproximately half way between the first two backs; and a newquasielliptical back with ordinates greater than the ellipse oftheelliptical back at all points except at the ends and the middle Fig.2 shows a developed section of any of the novel forms of my blade withminor modifications which it may be desirable to make near the leadingand trailing edges; and V Fig. 3 shows a developedblade section which isused in the formulation of a general equation employed in arriving atthe developed blade section of the present invention.

By formulating a general equation for determining the location of thefirst appearance of burbling cavitation I have been enabled to arrive atthe equation which expresses the conditions under which the pressure onthe suction or back side of the blade will be approximately uniform.Since a' short method in the formulation of the general equation isdesired,anumber of simplifications are made, which a priori werebelieved to be reasonable and aposteriori were found to be Justified.These simplifications are as follows. Only the case of uniform motion isconsidered. Over the pertinent area from near the leading edge to nearthe trailing edge the velocity relative to the blade is considereduniform. Over the pertinent area the stream lines are consideredapproximately'paraliel to each other. The following physical statementsare V=velccity and direction of P relative to'the blade. The directionmust obviously be tangent to the blade. Note that on the suction side ofthe blade V must always be greater than w, being compounded of W plusthe circulation velocity.

S=the velocity of P in space.

N=the component of S which is normal to the blade.

considered correct for the present purpose. Liquid in which a body issubmerged exerts a pressure on it. The pressure can be considered as.

being-exerted by the liquid particles in immediate contact with theapproximately stagnant boundary layer of liquid that clings tothe-body.

The particles outside those mentioned above merely increase or decreasethe pressure on the latter; and, if the stream lines are approximatelyparallel. do not change the relative pressure exerted by a particle incontact with the body (or boundary layer) as it flows past the body.Consequently, if the relative pressure exerted on a body by a particlewhich fiowspast it but always in contact with it (or the boundary layer)is determined, the loeation'of the lowest pressure can be determined. Ita particle. of liquid is being accelerated a force is involved. I In thecase of a submerged propeller blade the forces of gravity and cohesioncan be ignored and, therefore, the remainingforce is a difference inpressure. A particle of liquid moving relative to but in contact with asubmerged body has no' relative velocity towards or away from that body.but may wards the body, it indicates that the pressure at the body isless than-in the surrounding liquid:

' and'vice versa.

Reference is now made to Fig. 3 of the drawing w to show the manneremployed in formulating the general equation by "which the location ofthe first appearance of burbling cavitation is deterblade.

.o=angle between V and W .(reversed).

p=angle between S and V.

Since V is always greater than W on the suction side, N must always liebetween W and S; though mathematically it would make, no difference onwhich side of S, N lies; for in any case:

1v=s sin ,9 Eq. 1 Now by a law of trigonometry; Y

' sin B sin 0 2 Therefore: v

. I sin fl=- 2 0 q-- Hence:

N=W sin 0 1 Eq; 4 The rate of change of N with respect to 0 is:

dN 1 W cos 0 Eq. 5

Now:

d0 V Eq. 6

Multiplying Equations 5 and 6, we get:

dN da dN WV cos 0 w m-ar -R 7 But g dt

=the component of acceleration in space normal is the result of apressure at the blade above or 4 below that of the surrounding fluid.The total pressure at the blade is the pressure of the surrounding fluidplus or minus this acceleration pressure. Whether or not burbling occursdepends upon the total pressure at the blade.

From a consideration of the general equation Eq. 8 'it can be shownthat. underusual operating conditions, burbling cavitation'on the backof a blade will begin, in the case of an ogival blade,-at a point on theback where the curvature tion should give an approximately uniform suc-'of the blade is tangent to the direction of motion of the blade relativeto undisturbed water; and, in the case of airfoil blades, burblingcavitation will begin forward of that point of tangency. The

reason for this difierence is stated in section 4C of my articleentitled Cavitation on marine propellers appearing in the Transactionsof the American Society of Mechanical Engineers, vol. 59, No. 5, July1937, pages 409-431. Theimportant thing, however, to note in connectionwith the present invention'is that the acceleration A varies over theseblade sections withthe result that there cannot be a substantiallyuniform suction on the blade backs. This necessarily. follows from thefact that an acceleration pressure corresponds to each acceleration andthat the total pressure at the blade is the pressure of the surroundingfluid plus or minus this acceleration pressure. Whether or notburblingoccurs depend upon the total pressure at the blade.

If now the pressure distribution on the suction side or back of theblade is to be approximately uniform,. the acceleration pressure andhence A must be constant with the result that the general equation Eq. 8hereinbefore' discussed takes the form cos constant In this latterequation R at any point on the back of the blade is the radius ofcurvature of the developed section at this point, and 0 is the anglebetween the tangent to the blade at that point and the direction of flowof the undisturbed water relative to the blade, the tangent of courselying in the plane of thedeveloped section. If on a developed section ofthe blade the curve of the back thereof be represented by the equationthen equation 9 can be put'into the diiierential form; a

. 1 l= a* e en" Q] a.

. y 17: Equation 11 has not been solved, but I have studied itthoroughly and recognize it represents a figure strongly resembling anellipse.

=constant Eq. 11

'Thus, consider a conventional blade wherein any developed sectionthereof shows a circular arc backas at I (Fig. 1) which has come to'bedesignated an ogival back in the marine propeller art. A littleconsideration will make it clear that,since in this case R is constant,

' cos is not constant but decreases from a maximumvalue in. the middle:of the blinds: to minimum values'at the leading and! trailing edges.Since the suction decreases with decreasing, values of cos 0 Rissolbwimm that'mmitm evmana appteln um Ag; dufi, inom-aniuaitnum inwith 1111 nae'flm lim- Wm v i h'ualmu:

One of these simplifying assumptions was that from near the leading edgeto near the trailin edge the velocity vector of a liquid particle incontact with the boundary layer was constant in magnitude though ofcourse varying in direction.

This assumption was merely a device to render the mathematics tractable.As a matter both of theory and of physical fact it is known, however,that the magnitude of that vector varies also, being less near theleading and trailing edges. The shortening of this vector wouldtherefore decrease the suction near the leading and trailingedges. Tooffset or prevent decreased suction from this cause, a value of cos 0 isneeded which increases near the edges. As pointed out hereinbefore theellipse has such characteristics.

Thus, by purely theoretical, a priori reasoning, I was led to theconclusion that an elliptical back on any developed blade section wouldproduce a practically uniform suction and would resist the onset ofburbling cavitation longer than either the standard ogival backgenerally used or the airfoil backsometimes used. By blade with anairfoil back is meant a blade whose suction side has a shape similar tothat generally used on the suction side of airplane wings.

Following this theoretical reasoning, a number of foils were made, thedeveloped sections .of which had elliptical backs and the pressuredistribution measured experimentally in a wind tunnel. Up to about a 6angle of attack they had a substantially uniform suction over the backwith no prominent peak of suction thus differing markedly from eitherthe conventional ogival or airfoil backs. Since a marine propellerrarely reaches an angle'of attack as great as 5, except at the moment ofstarting, this was satisfactory.

Next .a standardi model. marine screw propeller, which suitered. badlyfrom: cavitation, was duplicatedi in every noanect except the newpropeilen'wasi provided with back: which. appeared elliptieall i'm intheir: develhnedl cross sections;v 'Ilhlsruuvell 1m waa them.

tested! i'm a variable pressure water lit. nesistedl burbli'ng: in than;the standard prior: anti pmpellbm; emit, at: the: slim ratios practicallfair pm; time new,-

wherein the backs were substantially elliptical in shape in theirdeveloped cross sections accomplish the purpose of the presentinvention, but

pended described.

also blades wherein the backs in their developed cross sections closelyapproximated an ellipse.

In Fig. 1 of the drawing there are shown superimposed on one another forcomparison and clarifying purposes four developed sections takenrespectivelyon four separate blades at the same but any convenientradius. The blades may form a part of a marine screw propeller or awater turbine screw propeller; and their curved section portions in allcases denote the backor suction side of the blade.

The standard, prior art, ogival back is indicated by the referencecharacter I; and the elliptical back of the present invention by thereference character 2. Quasi-elliptical backs 3 and 4 which closely approximate that of the. ellipse 2 are also considered novel and satisfythe requirements of the present invention. It will be observed that thequasi-elliptical back 3 lies approximately halfway between the prior artogival back I and the trueelliptical back 2 and represents anapproximate solution of Equation 11 set forth hereinbefore. Thequasi-elliptical back 4 has ordinates greater than those of the ellipseat all points except at the ends and middle of the latter. This back 4is intended to give an even closer approximation to a substantiallyuniform suction than is obtained by the ellipse '2. .In Fig. 2 of thedrawing there are shown minor modifications which maybe made near theleading and trailing edges of any of my new and novel blade forms inorder to further improve their operating characteristics. If it is founddesirable to modify any of my novel blade sections in the mannerdepicted in Fig. 2 it will be seen that the blade as modified has forits major portion an ellipf tical or quasielliptical back. 4

In Figs. 1 and 2 of the drawing the pressure side or face [of thevarious developed blade sections are shownas formed by the major axis ofThe .invention herein described and claimed may be-used and/ormanufactured by or for the Govemment of the United States of- Americafor governmental purposes without the payment of any royalties thereonor therefor.

I claim:

1. A blade adapted for movement in a liquid fluid medium, said bladehaving a back which in any developed section of theblade lies at leastfor its major portion substantially along a curve represented by thedifferential equation dy a +(s) 1 whereby to provide a back which delaysthe occurrence of burbling cavitation.

2. A blade adapted for movement in a liquid fluid medium, said bladehaving a back which in any developed section of the blade lies at leastfor its major portion substantially along a curve the ordinates of whichare greater than those of an ellipse at all points except at the endsand middle of the latter.

3. A blade adapted for movement in a liquid fluid medium, saidblade inany developed section thereof having a back which lies at least for itsmajor portion along an ellipm and a face which lies at least for itsmajor portion along the major axis of the ellipse.

4. A blade adapted formovement in a liquid fluid medium, said bladehaving a back which in any developed section of the blade has at least apartthereof substantially defined by the major portion of a semi-ellipsewhich has for its base the major axis of the ellipse.

5. A blade adapted for movement in a liquid fluid medium, said bladehaving a back which .in any developed section of the blade has at Jugatediameter inclined to the major axis, for

example, at an angle representing the average angle of attack; a chordparallel to the conjugate diameter; or 'a curved line to give theslightly concave pressure face sometimes used.

According to the provisions of the patent statutes I have set forth theprinciple and mode.

ellipse.

least a part thereof substantially deflned by the major portion of asemi-quasi ellipse, the major axis of which coincides with the majoraxis of an ellipse andthe end and middle ordinates of which are those ofthe ellipse.

6. A blade adapted for "movement in a liquid fluid medium, said bladehaving a back which in any developedsection of the blade has at least apart thereof substantially defined by the major portion 'of a semi-quasiellipse which has for its base the major axis of an ellipse and whichhas an ordinate at its middle which is that of said LYBRAND B. SMITH.

claims the invention may be practiced otherwise than as-speciflcallyillustrated and

